المؤلفون: Gil', Michael

مصطلحات موضوعية: keyword:Banach space, keyword:differential equation, keyword:linear nonautonomous equation, keyword:exponential stability, keyword:commutator, keyword:parabolic equation, msc:34G10, msc:35B35, msc:35K51, msc:47D06

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/151662

المؤلفون: Mizukami, Masaaki, Tanaka, Yuya

مصطلحات موضوعية: keyword:chemotaxis, keyword:Lotka–Volterra, keyword:finite-time blow-up, msc:35B44, msc:35K51, msc:92C17

وصف الملف: application/pdf

Relation: mr:MR4563033; zbl:Zbl 07675591; reference:[1] Baldelli, L., Filippucci, R.: A priori estimates for elliptic problems via Liouville type theorems.Discrete Contin. Dyn. Syst. Ser. S 13 (7) (2020), 1883–1898. MR 4097623; reference:[2] Black, T., Lankeit, J., Mizukami, M.: On the weakly competitive case in a two-species chemotaxis model.IMA J. Appl. Math. 81 (5) (2016), 860–876. MR 3556387, 10.1093/imamat/hxw036; reference:[3] Cieślak, T., Winkler, M.: Finite-time blow-up in a quasilinear system of chemotaxis.Nonlinearity 21 (5) (2008), 1057–1076. MR 2412327, 10.1088/0951-7715/21/5/009; reference:[4] Fuest, M.: Approaching optimality in blow-up results for Keller-Segel systems with logistic-type dampening.NoDEA Nonlinear Differential Equations Appl. 28 (16) (2021), 17 pp. MR 4223515; reference:[5] Mizukami, M.: Boundedness and stabilization in a two-species chemotaxis-competition system of parabolic-parabolic-elliptic type.Math. Methods Appl. Sci. 41 (1) (2018), 234–249. MR 3745368, 10.1002/mma.4607; reference:[6] Mizukami, M., Tanaka, Y., Yokota, T.: Can chemotactic effects lead to blow-up or not in two-species chemotaxis-competition models?.Z. Angew. Math. Phys. 73 (239) (2022), 25 pp. MR 4500792; reference:[7] Stinner, C., Tello, J.I., Winkler, M.: Competitive exclusion in a two-species chemotaxis model.J. Math. Biol. 68 (7) (2014), 1607–1626. MR 3201907, 10.1007/s00285-013-0681-7; reference:[8] Tello, J.I., Winkler, M.: Stabilization in a two-species chemotaxis system with a logistic source.Nonlinearity 25 (5) (2012), 1413–1425. MR 2914146, 10.1088/0951-7715/25/5/1413; reference:[9] Tu, X., Qiu, S.: Finite-time blow-up and global boundedness for chemotaxis system with strong logistic dampening.J. Math. Anal. Appl. 486 (1) (2020), 25 pp. MR 4053055; reference:[10] Winkler, M.: Finite-time blow-up in low-dimensional Keller-Segel systems with logistic-type superlinear degradation.Z. Angew. Math. Phys. 69 (69) (2018), 40 pp. MR 3772030

الاتاحة: http://hdl.handle.net/10338.dmlcz/151568

المؤلفون: Laurençot, Philippe, Matioc, Bogdan-Vasile

مصطلحات موضوعية: keyword:cross diffusion, keyword:weak-strong uniqueness, keyword:relative entropy, msc:35A02, msc:35K51, msc:35K65, msc:35Q35

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/151567

المؤلفون: Li, Yanqiu, Jiang, Juncheng

مصطلحات موضوعية: keyword:activator-inhibitor model, keyword:cubic polynomial source, keyword:Turing pattern, keyword:global stability, keyword:weakly linear coupling, msc:35B32, msc:35B35, msc:35B40, msc:35K51, msc:35Q92, msc:92C15

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/147595

المؤلفون: Jüngel, Ansgar

مصطلحات موضوعية: keyword:Strongly coupled parabolic systems, local existence of solutions, global existence of solutions, gradient flow, duality method, boundedness-by-entropy method, nonlinear Aubin-Lions lemma, Kullback-Leibler entropy, msc:35B65, msc:35K51, msc:35K57

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/703046

المؤلفون: Šamajová, Helena

مصطلحات موضوعية: keyword:Nonlinear partial differential equation, parabolic type equation, delayed equation, system of partial differential equation, initial problem, msc:35K51, msc:35K55, msc:35K61

وصف الملف: application/pdf

Relation: reference:[1] Benhammouda, B., Vazquez-Leal, H.: A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations., SpringerPlus, (2016), 5, 1723. DOI 10.1186/s40064-016-3386-8. 10.1186/s40064-016-3386-8; reference:[2] Khan, Y., Svoboda, Z., Šmarda, Z.: Solving certain classes of Lane-Emden type equations using the differential transformation method., Advances in Difference Equations, 174, (2012). MR 3016691; reference:[3] Odibat, Z. M., Bertelle, C., Aziz-Alaouic, M. A., Duchampd, H. E. G.: A multi-step differential transform method and application to non-chaotic or chaotic systems., Computers and Mathematics with Applications, 59, (2010), pp. 1462-1472. MR 2591936, 10.1016/j.camwa.2009.11.005; reference:[4] Odibat, Z. M., Kumar, S., Shawagfeh, N., Alsaedi, A., Hayat, T.: A study on the convergence conditions of generalized differential transform method., Mathematical Methods in the Applied Sciences, 40, (2017), pp 40-48. MR 3583033, 10.1002/mma.3961; reference:[5] Polyanin, A. D., Zhurov, A. I.: Functional constraints method for constructing exact solutions to delay reactiondiffusion equations and more complex nonlinear equations., Commun. Nonlinear Sci. Numer. Simulat., 19, (2014), pp 417-430. MR 3111621, 10.1016/j.cnsns.2013.07.017; reference:[6] Rebenda, J., Šmarda, Z.: A differential transformation approach for solving functional differential equations with multiple delays., Commun. Nonlinear Sci. Numer. Simulat., 48, (2017), pp. 246-257. MR 3607372, 10.1016/j.cnsns.2016.12.027; reference:[7] Rebenda, J., Šmarda, Z., Khan, Y.: A New Semi-analytical Approach for Numerical Solving of Cauchy Problem for Differential Equations with Delay., FILOMAT, 31, (2017), pp. 4725-4733. MR 3725533, 10.2298/FIL1715725R

الاتاحة: http://hdl.handle.net/10338.dmlcz/703053

المؤلفون: Mizukami, Masaaki

مصطلحات موضوعية: keyword:Chemotaxis, signal-dependent sensitivity, logistic term, global existence, msc:35A01, msc:35K51, msc:92C17

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Relation: reference:[1] Bellomo, N., Bellouquid, A., Tao, Y., Winkler, M.: Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues., Math. Models Methods Appl. Sci., 25, pp. 1663–1763, 2015. MR 3351175, 10.1142/S021820251550044X; reference:[2] Cao, X.: Global bounded solutions of the higher-dimensional Keller–Segel system under smallness conditions in optimal spaces., Discrete Contin. Dyn. Syst., 35, pp. 1891–1904, 2015. MR 3294230, 10.3934/dcds.2015.35.1891; reference:[3] Fujie, K.: Boundedness in a fully parabolic chemotaxis system with singular sensitivity., J.Math. Anal. Appl., 424, pp. 675–684, 2015. MR 3286587, 10.1016/j.jmaa.2014.11.045; reference:[4] Fujie, K.: Study of reaction-diffusion systems modeling chemotaxis., PhD thesis, Tokyo University of Science, 2016.; reference:[5] Fujie, K., Senba, T.: Global existence and boundedness of radial solutions to a two dimensional fully parabolic chemotaxis system with general sensitivity., Nonlinearity, 29, pp. 2417–2450, 2016. MR 3538418, 10.1088/0951-7715/29/8/2417; reference:[6] Fujie, K., Senba, T.: A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system., preprint. MR 3816648; reference:[7] He, X., Zheng, S.: Convergence rate estimates of solutions in a higher dimensional chemotaxis system with logistic source., J. Math. Anal. Appl., 436, pp. 970–982, 2016. MR 3446989, 10.1016/j.jmaa.2015.12.058; reference:[8] Horstmann, D., Wang, G.: Blow-up in a chemotaxis model without symmetry assumptions., Eur. J. Appl. Math., 12, pp. 159–177, 2001. MR 1931303, 10.1017/S0956792501004363; reference:[9] Lankeit, J.: A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivity., Math. Methods Appl. Sci., 39, pp. 394–404, 2016. MR 3454184, 10.1002/mma.3489; reference:[10] Lankeit, J., Winkler, M.: A generalized solution concept for the Keller–Segel system with logarithmic sensitivity: global solvability for large nonradial data., NoDEA, Nonlinear Differ. Equ. Appl., 24, No. 4, Paper No. 49, 33 p., 2017. MR 3674184, 10.1007/s00030-017-0472-8; reference:[11] Mizukami, M.: Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity., Discrete Contin. Dyn. Syst. Ser. B, 22, pp. 2301–2319, 2017. MR 3664704; reference:[12] Mizukami, M.: Improvement of conditions for asymptotic stability in a two-species chemotaxis competition model with signal-dependent sensitivity., submitted, arXiv:1706.04774[math.AP]. MR 3664704; reference:[13] Mizukami, M., Yokota, T.: Global existence and asymptotic stability of solutions to a two-species chemotaxis system with any chemical diffusion., J. Differential Equations, 261, pp. 2650–2669, 2016. MR 3507983, 10.1016/j.jde.2016.05.008; reference:[14] Mizukami, M., Yokota, T.: A unified method for boundedness in fully parabolic chemotaxis systems with signal-dependent sensitivity., Math. Nachr., to appear. MR 3722501; reference:[15] Nagai, T., Senba, T., Yoshida, K.: Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis., Funkcial. Ekvac., 40, pp. 411–433, 1997. MR 1610709; reference:[16] Negreanu, M., Tello, J. I.: On a two species chemotaxis model with slow chemical diffusion., SIAM J. Math. Anal., 46, pp. 3761–3781, 2014. MR 3277217, 10.1137/140971853; reference:[17] Negreanu, M., Tello, J. I.: Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant., J. Differential Equations, 258, pp. 1592–1617, 2015. MR 3295594, 10.1016/j.jde.2014.11.009; reference:[18] Winkler, M.: Aggregation vs. global diffusive behavior in the higher-dimensional Keller–Segel model., J. Differential Equations, 248, pp. 2889–2905, 2010. MR 2644137, 10.1016/j.jde.2010.02.008; reference:[19] Winkler, M.: Global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening., J. Differential Equations, 257, pp. 1056–1077, 2014. MR 3210023, 10.1016/j.jde.2014.04.023; reference:[20] Zhang, Q., Li, X.: Global existence and asymptotic properties of the solution to a two-species chemotaxis system., J. Math. Anal. Appl., 418, pp. 47–63, 2014. MR 3198865, 10.1016/j.jmaa.2014.03.084

الاتاحة: http://hdl.handle.net/10338.dmlcz/703018

المؤلفون: Yousefnezhad, Mohsen, Mohammadi, Seyyed Abbas, Bozorgnia, Farid

مصطلحات موضوعية: keyword:prey-predator model, keyword:prey-taxis, keyword:free boundary, keyword:classical solutions, keyword:global existence, msc:35K51, msc:35K55, msc:35K57, msc:35K59, msc:35R35, msc:92B05, msc:92D25

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Relation: mr:MR3795243; zbl:Zbl 06890302; reference:[1] Ainseba, B. E., Bendahmane, M., Noussair, A.: A reaction-diffusion system modeling predator-prey with prey-taxis.Nonlinear Anal., Real World Appl. 9 (2008), 2086-2105. Zbl 1156.35404, MR 2441768, 10.1016/j.nonrwa.2007.06.017; reference:[2] Bozorgnia, F., Arakelyan, A.: Numerical algorithms for a variational problem of the spatial segregation of reaction-diffusion systems.Appl. Math. Comput. 219 (2013), 8863-8875. Zbl 1291.65257, MR 3047783, 10.1016/j.amc.2013.03.074; reference:[3] Bunting, G., Du, Y., Krakowski, K.: Spreading speed revisited: analysis of a free boundary model.Netw. Heterog. Media 7 (2012), 583-603. Zbl 1302.35194, MR 3004677, 10.3934/nhm.2012.7.583; reference:[4] Chen, X., Friedman, A.: A free boundary problem arising in a model of wound healing.SIAM J. Math. Anal. 32 (2000), 778-800. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/147186

المؤلفون: Zhigun, Anna (Dr.), Surulescu, Christina (Prof. Dr.), Hunt, Alexander

مصطلحات موضوعية: global existence, go-or-grow dichotomy, Quantitative Biology::Tissues and Organs, Physics::Medical Physics, msc:35K59, weak solution, msc:35K57, Quantitative Biology::Cell Behavior, msc:35K51, Mathematics - Analysis of PDEs, msc:35K65, msc:35Q92, msc:35K20, FOS: Mathematics, cancer cell invasion, msc:92C17, ddc:510, parabolic system, haptotaxis, msc:35B45, degenerate diffusion, 35B45, 35D30, 35K20, 35K51, 35K57, 35K59, 35K65, 35Q92, 92C17, msc:35D30, Analysis of PDEs (math.AP)

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URL الوصول: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::94639f84e94885d7a59b5c43dde328ed

المؤلفون: Wehbe, Charbel

مصطلحات موضوعية: keyword:Caginalp phase-field system, keyword:Dirichlet boundary conditions, keyword:well-posedness, keyword:long time behavior of solution, keyword:global attractor, keyword:exponential attractor, keyword:Maxwell-Cattaneo law, keyword:logarithmic potential, msc:35B40, msc:35B41, msc:35G30, msc:35K51, msc:35K55, msc:35Q53, msc:45K05, msc:80A20, msc:80A22, msc:92D50

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Relation: mr:MR3396470; zbl:Zbl 06486916; reference:[1] Babin, A., Nicolaenko, B.: Exponential attractors for reaction-diffusion systems in an unbounded domain.J. Dyn. Differ. Equations 7 567-590 (1995). MR 1362671, 10.1007/BF02218725; reference:[2] Brochet, D., Hilhorst, D.: Universal attractor and inertial sets for the phase field model.Appl. Math. Lett. 4 59-62 (1991). Zbl 0773.35028, MR 1136614, 10.1016/0893-9659(91)90076-8; reference:[3] Brochet, D., Hilhorst, D., Chen, X.: Finite dimensional exponential attractor for the phase field model.Appl. Anal. 49 (1993), 197-212. Zbl 0790.35052, MR 1289743, 10.1080/00036819108840173; reference:[4] Brochet, D., Hilhorst, D., Novick-Cohen, A.: Finite-dimensional exponential attractor for a model for order-disorder and phase separation.Appl. Math. Lett. 7 83-87 (1994). Zbl 0803.35076, MR 1350381, 10.1016/0893-9659(94)90118-X; reference:[5] Caginalp, G.: An analysis of a phase field model of a free boundary.Arch. Ration. Mech. Anal. 92 205-245 (1986). Zbl 0608.35080, MR 0816623, 10.1007/BF00254827; reference:[6] Caginalp, G.: The role of microscopic anisotropy in the macroscopic behavior of a phase boundary.Ann. Phys. 172 136-155 (1986). Zbl 0639.58038, MR 0912765, 10.1016/0003-4916(86)90022-9; reference:[7] Cherfils, L., Miranville, A.: Some results on the asymptotic behavior of the Caginalp system with singular potentials.Adv. Math. Sci. Appl. 17 107-129 (2007). Zbl 1145.35042, MR 2337372; reference:[8] Conti, M., Gatti, S., Miranville, A.: Asymptotic behavior of the Caginalp phase-field system with coupled dynamic boundary conditions.Discrete Contin. Dyn. Syst., Ser. S 5 485-505 (2012). Zbl 1244.35067, MR 2861821, 10.3934/dcdss.2012.5.485; reference:[9] Fabrie, P., Galusinski, C.: Exponential attractors for partially dissipative reaction system.Asymptotic Anal. 12 329-354 (1996). MR 1402980, 10.3233/ASY-1996-12403; reference:[10] Gajewski, H., Zacharias, K.: Global behaviour of a reaction-diffusion system modelling chemotaxis.Math. Nachr. 195 (1998), 77-114. Zbl 0918.35064, MR 1654677, 10.1002/mana.19981950106; reference:[11] Grasselli, M., Miranville, A., Pata, V., Zelik, S.: Well-posedness and long time behavior of a parabolic-hyperbolic phase-field system with singular potentials.Math. Nachr. 280 1475-1509 (2007). Zbl 1133.35017, MR 2354975, 10.1002/mana.200510560; reference:[12] Kufner, A., John, O., Fučík, S.: Function Spaces.Monographs and Textsbooks on Mechanics of Solids and Fluids. Mechanics: Analysis. Noordhoff International Publishing, Leyden Academia, Prague (1977). MR 0482102; reference:[13] Landau, L. D., Lifschitz, E. M.: Course of Theoretical Physics. Vol. 1.Mechanics. Akademie Berlin German (1981).; reference:[14] Miranville, A.: Exponential attractors for a class of evolution equations by a decomposition method.C. R. Acad. Sci., Paris, Sér. I, Math. 328 145-150 (1999), English. Abridged French version. Zbl 1141.35340, MR 1669003; reference:[15] Miranville, A.: On a phase-field model with a logarithmic nonlinearity.Appl. Math., Praha 57 (2012), 215-229. Zbl 1265.35139, MR 2984601, 10.1007/s10492-012-0014-y; reference:[16] Miranville, A.: Some mathematical models in phase transition.Discrete Contin. Dyn. Syst., Ser. S 7 271-306 (2014). Zbl 1275.35048, MR 3109473, 10.3934/dcdss.2014.7.271; reference:[17] Miranville, A., Quintanilla, R.: A generalization of the Caginalp phase-field system based on the Cattaneo law.Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71 2278-2290 (2009). Zbl 1167.35304, MR 2524435, 10.1016/j.na.2009.01.061; reference:[18] Miranville, A., Quintanilla, R.: Some generalizations of the Caginalp phase-field system.Appl. Anal. 88 877-894 (2009). Zbl 1178.35194, MR 2548940, 10.1080/00036810903042182; reference:[19] Miranville, A., Zelik, S.: Robust exponential attractors for Cahn-Hilliard type equations with singular potentials.Math. Methods Appl. Sci. 27 (2004), 545-582. Zbl 1050.35113, MR 2041814, 10.1002/mma.464; reference:[20] Miranville, A., Zelik, S.: Attractors for dissipative partial differential equations in bounded and unbounded domains.C. M. Dafermos et al. Handbook of Differential Equations: Evolutionary Equations. Vol. IV Elsevier/North-Holland Amsterdam 103-200 (2008). Zbl 1221.37158, MR 2508165; reference:[21] Temam, R.: Infinite-Dimensional Dynamical Systems in Mechanics and Physics.Applied Mathematical Sciences 68 Springer, New York (1997). Zbl 0871.35001, MR 1441312, 10.1007/978-1-4612-0645-3

الاتاحة: http://hdl.handle.net/10338.dmlcz/144313

المؤلفون: Christina Surulescu, Anna Zhigun, Aydar Uatay

مصطلحات موضوعية: General Mathematics, Quantitative Biology::Tissues and Organs, General Physics and Astronomy, msc:35K59, msc:35K57, 01 natural sciences, Haptotaxis, Quantitative Biology::Cell Behavior, msc:35K51, Mathematics - Analysis of PDEs, msc:35Q92, FOS: Mathematics, medicine, 0101 mathematics, msc:92C17, ddc:510, parabolic system, haptotaxis, 35B45, 35D30, 35K20, 35K51, 35K57, 35K59, 35K65, 35Q92, 92C17, msc:35D30, Strongly coupled, Degenerate diffusion, Physics, global existence, Applied Mathematics, Weak solution, 010102 general mathematics, Degenerate energy levels, Cancer, weak solution, medicine.disease, 010101 applied mathematics, Parabolic system, Classical mechanics, msc:35K65, msc:35K20, cancer cell invasion, msc:35B45, degenerate diffusion, Analysis of PDEs (math.AP)

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https://kluedo.ub.rptu.de/files/4232/ZSU_hapto.pdf

المؤلفون: Watanabe, Hiroshi, Shirakawa, Ken

مصطلحات موضوعية: keyword:approximation method, keyword:stability, keyword:energy-dissipative solution, msc:35K51, msc:35K67, msc:35K87, msc:35R06

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Relation: mr:MR3238848; zbl:Zbl 06362267; reference:[1] Ambrosio, L., Fusco, N., Pallara, D.: Functions of Bounded Variation and Free Discontinuity Problems.Oxford Mathematical Monographs Clarendon Press, Oxford (2000). Zbl 0957.49001, MR 1857292; reference:[2] Ito, A., Kenmochi, N., Yamazaki, N.: A phase-field model of grain boundary motion.Appl. Math. 53 (2008), 433-454. Zbl 1199.35138, MR 2469586, 10.1007/s10492-008-0035-8; reference:[3] Ito, A., Kenmochi, N., Yamazaki, N.: Weak solutions of grain boundary motion model with singularity.Rend. Mat. Appl., VII. Ser. 29 (2009), 51-63. Zbl 1183.35159, MR 2548486; reference:[4] Ito, A., Kenmochi, N., Yamazaki, N.: Global solvability of a model for grain boundary motion with constraint.Discrete Contin. Dyn. Syst., Ser. S 5 (2012), 127-146. Zbl 1246.35100, MR 2836555; reference:[5] Kobayashi, R., Warren, J. A., Carter, W. C.: A continuum model of grain boundary.Physica D 140 (2000), 141-150. MR 1752970, 10.1016/S0167-2789(00)00023-3; reference:[6] Moll, S., Shirakawa, K.: Existence of solutions to the Kobayashi-Warren-Carter system.Calc. Var. Partial Differ. Equ (2013), 1-36 DOI 10.1007/s00526-013-0689-2. MR 3268865, 10.1007/s00526-013-0689-2; reference:[7] Mosco, U.: Convergence of convex sets and of solutions of variational inequalities.Adv. Math. 3 (1969), 510-585. Zbl 0192.49101, MR 0298508, 10.1016/0001-8708(69)90009-7; reference:[8] Shirakawa, K., Watanabe, H.: Energy-dissipative solution to a one-dimensional phase field model of grain boundary motion.Discrete Contin. Dyn. Syst., Ser. S 7 (2014), 139-159. Zbl 1275.35132, MR 3082861, 10.3934/dcdss.2014.7.139; reference:[9] Shirakawa, K., Watanabe, H., Yamazaki, N.: Solvability of one-dimensional phase field systems associated with grain boundary motion.Math. Ann. 356 (2013), 301-330. Zbl 1270.35008, MR 3038131, 10.1007/s00208-012-0849-2; reference:[10] Watanabe, H., Shirakawa, K.: Qualitative properties of a one-dimensional phase-field system associated with grain boundary.GAKUTO Internat. Ser. Math. Sci. Appl. 36 (2013), 301-328. MR 3203495

الاتاحة: http://hdl.handle.net/10338.dmlcz/143863

المؤلفون: Graf, Isabell, Peter, Malte A.

مصطلحات موضوعية: keyword:periodic homogenization, keyword:two-scale convergence, keyword:carcinogenesis, keyword:reaction-diffusion system, keyword:surface diffusion, msc:35B10, msc:35B27, msc:35B45, msc:35K51, msc:35K58, msc:92C37

وصف الملف: application/pdf

Relation: mr:MR3238832; zbl:Zbl 06362251; reference:[1] Allaire, G.: Homogenization and two-scale convergence.SIAM J. Math. Anal. 23 1482-1518 (1992). Zbl 0770.35005, MR 1185639, 10.1137/0523084; reference:[2] Bakhvalov, N. S., Panasenko, G.: Homogenization: Averaging Processes in Periodic Media: Mathematical Problems in the Mechanics of Composite Materials.Translated from the Russian. Mathematics and Its Applications: Soviet Series 36 Kluwer Academic Publishers, Dordrecht (1989). MR 1112788; reference:[3] Bensoussan, A., Lions, J.-L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures.Studies in Mathematics and its Applications 5 North-Holland Publ. Company, Amsterdam (1978). Zbl 0404.35001, MR 0503330; reference:[4] Besong, D. 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الاتاحة: http://hdl.handle.net/10338.dmlcz/143847

المؤلفون: Väth, Martin

مصطلحات موضوعية: keyword:reaction-diffusion system, keyword:Signorini condition, keyword:unilateral obstacle, keyword:instability, keyword:asymptotic stability, keyword:parabolic obstacle equation, msc:34D20, msc:35B35, msc:35K51, msc:35K57, msc:35K86, msc:35K87, msc:47H05, msc:47H11, msc:47J20, msc:47J35

وصف الملف: application/pdf

Relation: mr:MR3238834; zbl:Zbl 06362253; reference:[1] Drábek, P., Kučera, M., Míková, M.: Bifurcation points of reaction-diffusion systems with unilateral conditions.Czech. Math. J. 35 (1985), 639-660. Zbl 0604.35042, MR 0809047; reference:[2] Eisner, J., Kučera, M., Väth, M.: Bifurcation points for a reaction-diffusion system with two inequalities.J. Math. Anal. Appl. 365 (2010), 176-194. Zbl 1185.35074, MR 2585089, 10.1016/j.jmaa.2009.10.037; reference:[3] Henry, D.: Geometric Theory of Semilinear Parabolic Equations.Lecture Notes in Mathematics 840 Springer, Berlin (1981). Zbl 0456.35001, MR 0610244, 10.1007/BFb0089647; reference:[4] Kim, I.-S., Väth, M.: The Krasnosel'skii-Quittner formula and instability of a reaction-diffusion system with unilateral obstacles.Submitted to Dyn. Partial Differ. Equ. 20 pages.; reference:[5] Kučera, M., Väth, M.: Bifurcation for a reaction-diffusion system with unilateral and {Neumann} boundary conditions.J. Differ. Equations 252 (2012), 2951-2982. Zbl 1237.35013, MR 2871789, 10.1016/j.jde.2011.10.016; reference:[6] Mimura, M., Nishiura, Y., Yamaguti, M.: Some diffusive prey and predator systems and their bifurcation problems.Bifurcation Theory and Applications in Scientific Disciplines (Papers, Conf., New York, 1977) O. Gurel, O. E. Rössler Ann. New York Acad. Sci. 316 (1979), 490-510. Zbl 0437.92027, MR 0556853, 10.1111/j.1749-6632.1979.tb29492.x; reference:[7] Turing, A. M.: The chemical basis of morphogenesis.Phil. Trans. R. Soc. London Ser. B 237 (1952), 37-72. 10.1098/rstb.1952.0012; reference:[8] Väth, M.: Ideal Spaces.Lecture Notes in Mathematics 1664 Springer, Berlin (1997). Zbl 0896.46018, MR 1463946, 10.1007/BFb0093548; reference:[9] Väth, M.: Continuity and differentiability of multivalued superposition operators with atoms and parameters. I.Z. Anal. Anwend. 31 (2012), 93-124. Zbl 1237.47065, MR 2899873, 10.4171/ZAA/1450; reference:[10] Ziemer, W. P.: Weakly Differentiable Functions. Sobolev Spaces and Functions of Bounded Variation.Graduate Texts in Mathematics 120 Springer, Berlin (1989). Zbl 0692.46022, MR 1014685, 10.1007/978-1-4612-1015-3

الاتاحة: http://hdl.handle.net/10338.dmlcz/143849

المؤلفون: Tian, Yanling

مصطلحات موضوعية: keyword:delayed diffusive predator-prey model, keyword:modified Leslie-Gower scheme, keyword:Holling-type II scheme, keyword:persistence, keyword:stability, keyword:eigenvalue, keyword:monotonous iterative sequence, msc:35B25, msc:35K51, msc:35K55, msc:92C40, msc:92D25

وصف الملف: application/pdf

Relation: mr:MR3183474; zbl:Zbl 06362223; reference:[1] Aziz-Alaoui, M. A., Okiye, M. Daher: Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes.Appl. Math. Lett. 16 (2003), 1069-1075. MR 2013074, 10.1016/S0893-9659(03)90096-6; reference:[2] Chen, B., Wang, M.: Qualitative analysis for a diffusive predator-prey model.Comput. Math. Appl. 55 (2008), 339-355. Zbl 1155.35390, MR 2384151, 10.1016/j.camwa.2007.03.020; reference:[3] Ko, W., Ryu, K.: Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge.J. Differ. Equations 231 (2006), 534-550. MR 2287896, 10.1016/j.jde.2006.08.001; reference:[4] Lindström, T.: Global stability of a model for competing predators: An extension of the Ardito & Ricciardi Lyapunov function.Nonlinear Anal., Theory Methods Appl. 39 (2000), 793-805. Zbl 0945.34037, MR 1733130; reference:[5] Murray, J. D.: Mathematical Biology, Vol. 1: An Introduction. 3rd ed.Interdisciplinary Applied Mathematics 17 Springer, New York (2002). Zbl 1006.92001, MR 1908418; reference:[6] Murray, J. D.: Mathematical Biology, Vol. 2: Spatial Models and Biomedical Applications. 3rd revised ed.Interdisciplinary Applied Mathematics 18 Springer, New York (2003). Zbl 1006.92002, MR 1952568; reference:[7] Nindjin, A. F., Aziz-Alaoui, M. A., Cadivel, M.: Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay.Nonlinear Anal., Real World Appl. 7 (2006), 1104-1118. Zbl 1104.92065, MR 2260902; reference:[8] Pao, C. V.: Dynamics of nonlinear parabolic systems with time delays.J. Math. Anal. Appl. 198 (1996), 751-779. Zbl 0860.35138, MR 1377823, 10.1006/jmaa.1996.0111; reference:[9] Ryu, K., Ahn, I.: Positive solutions for ratio-dependent predator-prey interaction systems.J. Differ. Equations 218 (2005), 117-135. MR 2174969, 10.1016/j.jde.2005.06.020; reference:[10] Tian, Y., Weng, P.: Stability analysis of diffusive predator-prey model with modified Leslie-Gower and Holling-type II schemes.Acta Appl. Math. 114 (2011), 173-192. Zbl 1216.35159, MR 2794080, 10.1007/s10440-011-9607-9; reference:[11] Upadhyay, R. K., Iyengar, S. R. K.: Effect of seasonality on the dynamics of 2 and 3 species prey-predator systems.Nonlinear Anal., Real World Appl. 6 (2005), 509-530. Zbl 1072.92058, MR 2129561; reference:[12] Wang, Y.-M.: Asymptotic behavior of solutions for a class of predator-prey reaction-diffusion systems with time delays.J. Math. Anal. Appl. 328 (2007), 137-150. Zbl 1112.35106, MR 2285539, 10.1016/j.jmaa.2006.05.020; reference:[13] Wang, W., Takeuchi, Y., Saito, Y., Nakaoka, S.: Prey-predator system with parental care for predators.J. Theoret. Biol. 241 (2006), 451-458. MR 2254918, 10.1016/j.jtbi.2005.12.008; reference:[14] Wu, J.: Theory and Applications of Partial Functional Differential Equations.Applied Mathematical Sciences 119 Springer, New York (1996). Zbl 0870.35116, 10.1007/978-1-4612-4050-1

الاتاحة: http://hdl.handle.net/10338.dmlcz/143631

المؤلفون: Suzuki, Takashi

مصطلحات موضوعية: keyword:tumor growth modeling, keyword:mean field theory, keyword:parabolic-ODE system, keyword:global-in-time existence, keyword:chemotaxis, msc:35K51, msc:35K57, msc:35Q92, msc:92C17, msc:92C50

وصف الملف: application/pdf

Relation: mr:MR2978266; zbl:Zbl 1265.35159; reference:[1] Anderson, A. R. A., Chaplain, M. A. J.: Continuous and discrete mathematical models of tumor-induced angeogenesis.Bull. Math. Biol. 60 (1998), 857-899. 10.1006/bulm.1998.0042; reference:[2] Anderson, A. R. A., Pitcairn, A. W.: Application of the hybrid discrete-continuum technique.Polymer and Cell Dynamics-Multiscale Modeling and Numerical Simulations, Birkhäuser, Basel, 2003, pp. 261-279.; reference:[3] Anderson, A. R. A., Quaranta, V.: Integrative mathematical oncology.Cancer 8 (2008), 227-234.; reference:[4] Anderson, A. R. A., Weaver, A. M., Cummings, R. T., Quaranta, V.: Tumor morphology and phenotypic evolution driven by selective pressure from the microenvironment.Cell 127 (2006), 905-915. 10.1016/j.cell.2006.09.042; reference:[5] Biler, P., Stańczy, R.: Mean field models for self-gravitating particles.Folia Matematica 13 (2006), 3-19. Zbl 1181.35290, MR 2675439; reference:[6] Childress, S., Percus, J. 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Wei Gakkotosho, Tokyo (2005), 121-136.; reference:[15] Kubo, A., Saito, N., Suzuki, T., Hoshino, H.: Mathematical modelds of tumor angiogenesis and simulations.Kokyuroku RIMS 1499 (2006), 135-146. MR 2320335; reference:[16] Kubo, A., Suzuki, T.: Asymptotic behavior of the solution to a parabolic ODE system modeling tumor growth.Differ. Integral Equ. 17 (2004), 721-736. MR 2074683; reference:[17] Kubo, A., Suzuki, T.: Mathematical models of tumour angiogenesisi.J. Comp. Appl. Math. 204 (2007), 48-55. MR 2320335, 10.1016/j.cam.2006.04.027; reference:[18] Levine, H. A., Sleeman, B. D.: A system of reaction and diffusion equations arising in the theory of reinforced random walks.SIAM J. Appl. Math. 57 (1997), 683-730. MR 1450846, 10.1137/S0036139995291106; reference:[19] Lions, J. L.: Quelques Méthodes de Résolution de Problèmes aux Limites Non Linéaires.Dunod-Gauthier-Villars, Paris (1969), French. MR 0259693; reference:[20] Murray, J. 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Zbl 1247.35001, MR 2510744; reference:[31] Suzuki, T., Takahashi, R.: Global in time solution to a class of tumour growth systems.Adv. Math. Sci. Appl. 19 (2009), 503-524. MR 2605731; reference:[32] Yang, Y., Chen, H., Liu, W.: On existence and non-existence of global solutions to a system of reaction-diffusion equations modeling chemotaxis.SIAM J. Math. Anal. 33 (1997), 763-785. MR 1884721, 10.1137/S0036141000337796

الاتاحة: http://hdl.handle.net/10338.dmlcz/142866

المؤلفون: Krejčí, Pavel, Panizzi, Lucia

مصطلحات موضوعية: keyword:parabolic system, keyword:regularity, keyword:uniqueness, msc:35A02, msc:35B65, msc:35K51, msc:35K59, msc:35K60

وصف الملف: application/pdf

Relation: mr:MR2833166; zbl:Zbl 1240.35234; reference:[1] Adams, R. A.: Sobolev Spaces. Pure and Applied Mathematics, Vol. 65.Academic Press New York-London (1975). MR 0450957; reference:[2] Barrett, J. W., Deckelnick, K.: Existence, uniqueness and approximation of a doubly-degenerate nonlinear parabolic system modelling bacterial evolution.Math. Models Methods Appl. Sci. 17 (2007), 1095-1127. Zbl 1144.35026, MR 2337432, 10.1142/S0218202507002212; reference:[3] Besov, O. V., Il'in, V. P., Nikol'skij, S. M.: Integral Representations of Functions and Imbedding Theorems. Scripta Series in Mathematics (Vol. I, Vol. II).V. H. Winston & Sons, John Wiley & Sons Washington/New York (1978), 1979; Russian version Nauka, Moscow, 1975. MR 0430771; reference:[4] Fasano, A., Hömberg, D., Panizzi, L.: A mathematical model for case hardening of steel.Math. Models Methods Appl. Sci. 19 (2009), 2101-2126. Zbl 1180.35277, MR 2588960, 10.1142/S0218202509004054; reference:[5] Griepentrog, J. A.: Maximal regularity for nonsmooth parabolic problems in Sobolev-Morrey spaces.Adv. Differ. Equ. 12 (2007), 1031-1078. Zbl 1157.35023, MR 2351837; reference:[6] Koshelev, A. I.: Regularity Problem for Quasilinear Elliptic and Parabolic Systems. Lecture Notes in Mathematics, 1614.Springer Berlin (1995). MR 1442954; reference:[7] Ladyzhenskaya, O. A., Solonnikov, V. A., Ural'ceva, N. N.: Linear and Quasi-linear Equations of Parabolic Type. American Mathematical Society Transl. 23.AMS Providence (1968).; reference:[8] Lions, J.-L.: Quelques méthodes de résolution des problemes aux limites non linéaires.Dunod/Gauthier-Villars Paris (1969), French. Zbl 0189.40603, MR 0259693; reference:[9] Lieberman, G. M.: Second Order Parabolic Differential Equations.World Scientific Publishing Co., Inc. Singapore (1996). Zbl 0884.35001, MR 1465184; reference:[10] Nečas, J.: Les méthodes directes en théorie des équations elliptiques.Academia Prague (1967). MR 0227584; reference:[11] Rodrigues, J. F.: A nonlinear parabolic system arising in thermomechanics and in thermomagnetism.Math. Models Methods Appl. Sci. 2 (1992), 271-281. Zbl 0763.35093, MR 1181337, 10.1142/S021820259200017X; reference:[12] Shilkin, T.: Classical solvability of the coupled system modelling a heat-convergent Poiseuille-type flow.J. Math. Fluid Mech. 7 (2005), 72-84. Zbl 1065.35135, MR 2127742, 10.1007/s00021-004-0112-z

الاتاحة: http://hdl.handle.net/10338.dmlcz/141598

المؤلفون: Jangveladze, Temur A., Kiguradze, Zurab V.

مصطلحات موضوعية: keyword:system of nonlinear integro-differential equations, keyword:magnetic field, keyword:asymptotics for large time, msc:35B40, msc:35K51, msc:35K55, msc:35Q61, msc:45K05, msc:74H40, msc:78A30

وصف الملف: application/pdf

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الاتاحة: http://hdl.handle.net/10338.dmlcz/140822

المؤلفون: Murakawa, Hideki

مصطلحات موضوعية: keyword:reaction-diffusion system approximation, keyword:degenerate parabolic problem, keyword:cross-diffusion system, msc:35K51, msc:35K55, msc:35K57, msc:35K65, msc:76S05, msc:80A22

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الاتاحة: http://hdl.handle.net/10338.dmlcz/140064